Numerical Experiments with a Variational Scheme for Attenuation-Correction for X-band Radar

The variational scheme developed and evaluated by Robin Hogan for S-band radar for estimating rain rate and detecting hail, is used here specifically for X-band application to correct the measured Zh and Zdr for attenuation due to mixed phase precipitation (rain mixed with wet ice/hail) which is an especially severe problem for lower power, short range radars. While a number of algorithms for attenuation-correction (based on differential propagation phase) are available at X-band when only rain occurs along the propagation path, there is no stable algorithm as yet when rain is mixed with wet ice/hail. Hence this paper is aimed at applying the variational scheme, which in its formulation, estimates the attenuation due to both rain and hail along the propagation path. We report on several numerical experiments with the variational code to optimize the attenuation-correction in mixed phase precipitation at X-band. The forward model was adapted from S to X-band based on scattering simulations. The measurement errors in Zdr and differential propagation phase for the particular X-band radar which we used (one of the CASA IP1 radars in Oklahoma) were adapted based on reflectivity and copolar correlation coefficient along the beam. This adjusts the weights given to Zdr and differential propagation phase in the cost function. We used the hail detection ratio (HDR) based on (Zh ,Zdr) to pre-identify hail along the path and thereby initialize the detection of hail in the variational scheme. This was followed by pre-estimating the “reflectivity weighted fraction of ice” using the “deviation from the rain line” methodology as an initialization for the “fraction of ice” in the variational scheme. The scheme then finds an optimal solution for attenuation-corrected Zh and Zdr due to rain+wet ice along the path. The preliminary improvements of the variational scheme using CASA X-band radar data in a convective storm with rain and wet hail are evaluated.